Uploading contracts to an online database should not take too long, and with the right solution, there should be a way to quickly drag and drop them into folders. Of course, the contract management team may want to give some thought as to how those folders are categorized. In some industries, it may make sense to classify them by agreement type, whereas in others they may need to be grouped by timeframe or date. It is obviously important to do what makes sense for your company and to ensure everyone understands the classification system that is instituted. With this sort of well-oiled system in place, it is a lot easier to keep a handle on things.

Divide and Conquer.
This is another area that is very industry-dependent, but it is highly unlikely that any company can afford to have an entire contract team devoted to managing one portfolio. More than likely, it is more realistic to divvy up the team and the contracts so that there is a leader for each relevant sphere. The entire team will obviously have to coordinate and communicate, but resources must be allocated in the most efficient manner possible. In turn, this will allow for several individuals to keep an eye on a smaller batch of contracts, thereby facilitating those periodic reviews.
Outsource the Tedium to Technology.